CN112184549B - Super-resolution image reconstruction method based on space-time transformation technology - Google Patents

Abstract

The invention discloses a super-resolution image reconstruction method based on space-time transformation technology, which divides the image into three components of R, G and B; and composes the R, G and B components of each low-resolution image sequence into vector l _R , l _G , l _B ; use the space-time transformation technology to construct the contribution matrix A _R , A _G , A _B of each high-resolution space-time point corresponding to the low-resolution space-time point; use the linear formula Ah of the high-resolution element to operate through the conjugate gradient algorithm = l to obtain the vectors h _R , h _G , h _B of the high time resolution image sequence; according to h _R , h _G and h _B values, use the iterative back projection method to reconstruct the spatial super-resolution, and obtain the super-resolution image sequence X R , X G and X _B corresponding to _R , _G and B components; X _R , X _G and X _B are synthesized to obtain a super-resolution image. The image reconstruction method in the present invention can effectively solve the problems of low image reconstruction resolution, low accuracy, and complex calculation, thereby obtaining an image with good quality; the operation is simple, the cost is low, and it has high robustness.

Description

Super-resolution image reconstruction method based on space-time transformation technology

technical field

The invention relates to the technical field of image reconstruction, in particular to a super-resolution image reconstruction method based on space-time transformation technology.

Background technique

Pixel resolution is a direct factor affecting image quality, and higher resolution is more conducive to further processing and synthesis of images. Super-resolution image reconstruction refers to combining several lower-resolution images to reconstruct an ultra-high-resolution image. Here "ultra" means that the super-resolution image reconstruction method can break through the existing sampling frequency control of traditional sensing devices. The resolution of a digital image not only represents the pixels of the image, but also represents the resolution ability of the image details. Image resolution is a key factor in measuring image detail. Image interpolation can arbitrarily enlarge or reduce the proportion of an image, but it does not mean improving or reducing its image resolution, while super-resolution image reconstruction is based on the data of the mutual movement of several lower-resolution images in the same scene, combining them into an image, making that image very high resolution. The biggest bright spot of this method is to reduce costs, while existing lower-resolution images can still be used.

In recent years, super-resolution image reconstruction has become a research hotspot in video surveillance, military and medical and other related fields. Zhan Yuli, Chi Jing et al. According to the fact that traditional images are prone to loss of detail data in the reconstruction process, or image edge distortion and noise are prone to occur when details are enhanced, they proposed to use cross-scale and feature combination methods to super-resolution images rate reconstruction. First, according to the cross-scale features of the image, the neighbor method is used to construct the mapping relationship between the pixels and the gradient characteristics between the high and low resolution images; then the initial input image is reconstructed by using the mapping relationship, and the height of the initial input image is obtained by the singular value thresholding method. The high-frequency data; finally, the high-frequency data is processed by block superposition using the gradient feature mapping method, and the obtained data is fused to the high-resolution image to obtain the final image. This method can effectively enhance image details, improve image resolution, and enhance visual effects, but the operation process is complicated and a lot of cost is wasted;

Xu Jun and Liu Hui's research found that traditional image synthesis in the medical field has a problem of low resolution, which seriously affects the accuracy of clinical diagnosis and treatment. Therefore, a non-local autoregressive learning method is proposed to reconstruct medical images. According to the unique non-local characteristics of medical images, a new model is constructed by using the autoregressive function and the classification dictionary obtained by clustering, and finally a reconstructed high-resolution image is obtained. This method greatly improves the resolution of medical images, but the calculation process is still too cumbersome and wastes a lot of time;

Yang Biao and Di Miao proposed to reconstruct the resolution of two or more images by means of block symmetric stacking based on the problems of slow speed and poor image quality in image reconstruction with current resolution. First, the ORB method is used to perform image registration processing on the lower-resolution image sequence, and then the processed image is reconstructed by PSyCo, and then the reconstructed image is processed by pixel gray maximum value fusion processing to obtain an ultra-high resolution image. The reconstruction image resolution of this method is high, but the reconstruction accuracy of the resolution image is low, which seriously affects the image quality.

Contents of the invention

In view of the above existing problems, the present invention aims to provide a super-resolution image reconstruction method based on spatio-temporal transformation technology, which can effectively solve the problems of low resolution, low accuracy and complex calculation of image reconstruction, thereby obtaining excellent image quality.

In order to achieve the above object, the technical scheme adopted in the present invention is as follows:

The super-resolution image reconstruction method based on space-time transformation technology, is characterized in that, comprises the following steps,

S1: Divide the image into three components of R, G and B by means of components;

S2: Compose the R, G and B components of each low-resolution image sequence into vectors l _R , l _G , l _B , where l _R , l _G , and l _B represent the vectors of all low-resolution observation values in the corresponding components ;

S3: Use the space-time transformation technology to construct the contribution matrices A _R , A _G , A _B of each high-resolution space-time point corresponding to the low-resolution space-time point;

S4: Use the linear formula Ah=l of high-resolution elements to obtain the vectors h _R , h _G , h _B of the high-time resolution image sequence; where, h _R , h _G , h _B represent all the reconstructed image frame sequences X different component vectors of unknown high-resolution values;

S5: Reconstruct the spatial super-resolution according to the h _R , h _G and h _B values obtained in step S4, and obtain X _R , X _G and X _B corresponding to the R, G and B components in the super-resolution image sequence;

S6: Combining R, G and B components X _R , X _G and X _B to finally obtain a super-resolution image.

Further, the specific operation of step S3 includes the following steps,

S31: Perform matching processing on the low-resolution image sequences to obtain N low-resolution image sequences, perform temporal and spatial downsampling on the observation models of the N low-resolution image sequences, and obtain N sampling matrices D ₁ and D ₂ based on temporal and spatial transformations, ..., D _N ;

S32: Find out that the object space will not change the coordinates of each point in the space with the movement of the field of view, and obtain the space-time coordinate transformation matrices T ₁ , T ₂ , ..., T _N of N low-resolution images;

S33: Obtain camera point spread functions H ₁ , H ₂ , ..., H _N of N low-resolution images, and time blur matrices M ₁ , M ₂ , ..., M _N corresponding to the low-resolution image sequences;

S34: Establish observation models of several images;

S35: From the observation model, it can be concluded that the relationship between the i-th low-resolution image sequence and the predicted high-resolution sequence X is Y _i =D _i M _i H _i T _i X+n _i , 1≤i≤N , where N _i represents the observation noise of the i-th low-resolution image; Y _i is also the contribution matrix A of the low-resolution spatio-temporal points corresponding to each high-resolution spatio-temporal point;

S36: The R, G and B components of the contribution matrix A of the low-resolution space-time point corresponding to each high-resolution space-time point are the contribution matrices A _R , A _G , A _B .

Further, in step S4, the vectors h _R , h _G , and h _B of the high-time resolution image sequence are obtained by using the conjugate gradient algorithm.

Further, the specific operation of using the conjugate gradient algorithm to obtain the vectors h _R , h _G , and h _B of the high-time resolution image sequence includes the following steps,

S41: According to the linear formula Ah=l of high-resolution elements, the least square image sequence model min E(h)=min{||Ah-l|| ² } can be obtained;

S42: Normalize the least square image sequence model to obtain the image sequence super-resolution reconstruction equation min E(h)=min{||Ah-l|| ² +α||WCh|| ² }; where , W represents the diagonal weight matrix function that records the expected normalization situation at each time point; α represents the overall normalization factor; C represents the matrix that records the space-time square valence derivative, which is selected as the laplace operator;

S43: Initially set β=0, h ₀ =0, b= ^AT l, r=b, p=b;

S44: Carry out iterative operation from k=1, 2..., wherein, the algorithm search direction is p=r+βp, q=(A ^T A+αC ^T W ^T WC)p; the algorithm search step size is α=r ^T r/p ^T p, the algorithm gradient is r ₀ = r, r = r ₀ -αq,

S45: Then obtain the actual search h _k =h _k-1 +αp, where h=h _R , h _G , h _B .

Further, step S5 performs spatial super-resolution reconstruction using an iterative back-projection method.

其中，m描述为迭代次数；p描述为在低分辨率图像中的帧数量；/>

描述为第m+1次进行迭代获得的超分辨率图像帧；/>

描述为第m次进行迭代获得的超分辨率图像帧；/>

描述为迭代反投影实践次数；/>

描述为/>

在低分辨率观测模型中实验获得的低分辨率图像帧；λ描述为梯度步长；f描述为参考帧；Δ描述为平方价微分的拉普拉斯算符。Further, the method of spatial super-resolution reconstruction using iterative back-projection can be expressed as

Among them, m is described as the number of iterations; p is described as the number of frames in the low-resolution image; />

Described as the super-resolution image frame obtained by the m+1th iteration; />

Described as the super-resolution image frame obtained by the mth iteration; />

Described as the number of iterative backprojection practices; />

described as />

A low-resolution image frame experimentally obtained in a low-resolution observation model; λ is described as the gradient step size; f is described as the reference frame; Δ is described as the Laplace operator of the quadratic valence differential.

The beneficial effects of the present invention are:

In the present invention, the super-resolution image reconstruction method based on the space-time transformation technology adopts the matching method to reconstruct the high-time-resolution image sequence, and uses the iterative back-projection method to perform the space-time super-resolution reconstruction process on the obtained sequence, and finally obtains the super-resolution The image has been verified by simulation experiments. This method is simple in calculation, fast in reconstruction speed, improves image resolution, and effectively solves problems such as deformation, noise, and blurring in the image reconstruction process.

Description of drawings

Fig. 1 is the observation model of several low-resolution images among the present invention;

Fig. 2 is for the image sequence reconstruction situation under the foreman rule in the simulation experiment of the present invention;

Fig. 3 is the image reconstruction situation based on actual text sequence in the simulation experiment of the present invention;

Fig. 4 is the comparison situation of foreman sequence iterative calculation in the emulation experiment of the present invention;

FIG. 5 is a comparison of iterative calculations based on actual text sequences in the simulation experiment of the present invention.

Detailed ways

In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

A super-resolution image reconstruction method based on space-time transformation technology, comprising the following steps,

S1: Divide the image into three components of R, G and B by means of components;

S2: Compose the R, G and B components of each low-resolution image sequence into vectors l _R , l _G , l _B , where l _R , l _G , and l _B represent the vectors of all low-resolution observation values in the corresponding components ;

S3: Use the space-time transformation technology to construct the contribution matrices A _R , A _G , A _B of each high-resolution space-time point corresponding to the low-resolution space-time point;

For some unclear space degradation functions such as linear and radial motion, you can try to find a coordinate space. The object space will not change the coordinates of each point in the space with the movement of the field of view, so you can use various coordinates in this space. This image restoration method completes image restoration, and then transforms back to the original image space, which is the basic process of image spatiotemporal transformation.

式中，P表示初始图像，(u，v)与(x，y)表示物空间与像空间的坐标，α(x，y)，β(u，v)，c_n(x，y)，b_n(u，v)，c_I2(x，y)，b_I2(u，v)分别表示相对应可逆函数点坐标，并在全部空间中α(x，y)≠0，β(u，v)≠0，P_I(·)可以进行傅里叶变换函数，得到

由此可见，时空坐标变换是一种既直接又简单的超分辨率图像重建方法，为提高后续图像重建精准度奠定基础。Linear motion will cause the spatial image to change, and the degree of spatial image change can be obtained through the system image field curvature and vertical and horizontal differences. If the image represents a certain form, it can be converted by spatial transformation to obtain

In the formula, P represents the initial image, (u, v) and (x, y) represent the coordinates of object space and image space, α(x, y), β(u, v), c _n (x, y), b _n (u, v), c _I2 (x, y), b _I2 (u, v) respectively represent the coordinates of the corresponding reversible function points, and in all spaces α(x, y)≠0, β(u, v)≠0, P _I (·) can perform Fourier transform function, get

It can be seen that the space-time coordinate transformation is a direct and simple super-resolution image reconstruction method, which lays the foundation for improving the accuracy of subsequent image reconstruction.

Specifically, in the present invention, using the space-time transformation technology to construct the contribution matrices A _R , A _G , and A _B of each high-resolution space-time point corresponding to the low-resolution space-time point includes the following steps,

S31: Perform matching processing on the low-resolution image sequences to obtain N low-resolution image sequences, perform temporal and spatial downsampling on the observation models of the N low-resolution image sequences, and obtain N sampling matrices D ₁ and D ₂ based on temporal and spatial transformations, ..., D _N ;

S32: Find out that the object space will not change the coordinates of each point in the space with the movement of the field of view, and obtain the space-time coordinate transformation matrices T ₁ , T ₂ , ..., T _N of N low-resolution images;

S33: Obtain camera point spread functions H ₁ , H ₂ , ..., H _N of N low-resolution images, and time blur matrices M ₁ , M ₂ , ..., M _N corresponding to the low-resolution image sequences;

S34: establish the observation model of several images, as shown in accompanying drawing 1, in accompanying drawing 1, n _i represents the observation noise of the ith low-resolution image;

S35: According to the observation model, it can be concluded that the relationship between the i-th low-resolution image sequence and the predicted high-resolution sequence X is Y _i =D _i M _i H _i T _i X+n _i , 1≤i≤N , where n _i represents the observation noise of the i-th low-resolution image; Y _i is also the contribution matrix A of the low-resolution spatio-temporal points corresponding to each high-resolution spatio-temporal point;

S36: The R, G and B components of the contribution matrix A of the low-resolution space-time point corresponding to each high-resolution space-time point are the contribution matrices A _R , A _G , A _B .

S4: Use the linear formula Ah=l of high-resolution elements to obtain the vectors h _R , h _G , h _B of the high-time resolution image sequence; where, h _R , h _G , h _B represent all the reconstructed image frame sequences X different component vectors of unknown high-resolution values;

Specifically, the vectors h _R , h _G , and h _B of the high-time resolution image sequence are obtained by using the conjugate gradient algorithm.

S41: According to the linear formula Ah=l of high-resolution elements, the least square image sequence model min E(h)=min{||Ah-l|| ² } can be obtained;

S42: Normalize the least square image sequence model to obtain the image sequence super-resolution reconstruction equation min E(h)=min{||Ah-l|| ² +α||WCh|| ² }; where , W represents the diagonal weight matrix function that records the expected normalization situation at each time point; α represents the overall normalization factor; C represents the matrix that records the space-time square valence derivative, which is selected as the laplace operator;

S43: Initially set β=0, h ₀ =0, b= ^AT l, r=b, p=b;

S44: Carry out iterative operation from k=1, 2..., wherein, the algorithm search direction is p=r+βp, q=(A ^T A+αC ^T W ^T WC)p; the algorithm search step size is α=r ^T r/p ^T p, the algorithm gradient is r ₀ = r, r = r ₀ -αq,

S45: Then obtain the actual search h _k =h _k-1 +αp, where h=h _R , h _G , h _B .

S5: Reconstruct the spatial super-resolution according to the h _R , h _G and h _B values obtained in step S4, and obtain X _R , X _G and X _B corresponding to the R, G and B components in the super-resolution image sequence;

Specifically, an iterative back-projection method is used for spatial super-resolution reconstruction.

其中，m描述为迭代次数；p描述为在低分辨率图像中的帧数量；/>

描述为第m+1次进行迭代获得的超分辨率图像帧；/>

描述为第m次进行迭代获得的超分辨率图像帧；/>

描述为迭代反投影实践次数；/>

描述为/>

在低分辨率观测模型中实验获得的低分辨率图像帧；λ描述为梯度步长；f描述为参考帧；Δ描述为平方价微分的拉普拉斯算符。The method of spatial super-resolution reconstruction using iterative back-projection can be expressed as

Among them, m is described as the number of iterations; p is described as the number of frames in the low-resolution image; />

Described as the super-resolution image frame obtained by the m+1th iteration; />

Described as the super-resolution image frame obtained by the mth iteration; />

Described as the number of iterative backprojection practices; />

described as />

A low-resolution image frame experimentally obtained in a low-resolution observation model; λ is described as the gradient step size; f is described as the reference frame; Δ is described as the Laplace operator of the quadratic valence differential.

S6: Combining R, G and B components X _R , X _G and X _B in a component matrix to finally obtain a super-resolution image.

Simulation:

In order to verify that the super-resolution image reconstruction method based on the space-time transformation technology in the present invention has high effectiveness, the present invention has carried out two groups of simulation experiments: the first group adopts the foreman rule image sequence of CIF mode, and the object movement of this sequence is relatively strong, Partial deformation and dislocation of the human face occurred, and the motion scene also changed; the second group is a text image sequence of real shooting. The motion scene contains Chinese characters, table lines, numbers, etc., and the camera will shake violently during the shooting process.

In the first group of simulation experiments, the 33rd frame of the foreman image sequence is set as the intermediate reference frame, and 6 frames of high-resolution initial images are obtained by sampling at a ratio of 3:1 in time. The Gaussian module performs convolution blurring; after that, 2:1 ratio sampling is performed in time to obtain 6 frames of low-resolution images; finally, bilinear interpolation is performed on the reference image frame, and it is used as a super-resolution image reconstruction Raw forecast data.

In the second group of simulation experiments, since the irregular sequence is used, one frame can be arbitrarily selected as an intermediate reference frame, and 6 frames of low-resolution images can be obtained using the same method as the first group of simulation experiments.

The three-dimensional reconstruction method of wheat grain image based on z-axis weight was used respectively (Three-dimensional wheat grain image based on z-axis weight; Reconstruction, Zhang Hongtao, Chang Yan, Tan Lian, et al. Acta Optics Sinica, 2019, 39(3): 127-135) , hereinafter referred to as method one, reconstructs the image with the super-resolution image reconstruction method based on the space-time transformation technology in the present invention, the results of the first group of simulation experiments are shown in Figure 2, where (a) is the initial high resolution Reference image, (b) is a low-resolution reference image, (c) is an image reconstructed by method 1, and (d) is an image reconstructed by the method of the present invention.

The results of the second group of simulation experiments are shown in Figure 3, where (a) is the initial high-resolution reference image, (b) is the low-resolution reference image, (c) is the image reconstructed by method 1, (d ) is an image reconstructed by the method of the present invention.

According to the above two sets of simulation experiments, the number of iterative calculations of the two methods is the same, and the parameter settings of each method are based on the basic principle that the quality of the reconstructed image is close to optimal, and the parameters that need to be strictly controlled are: Method 1 Correct the residual threshold δ ₀ The first group of simulation experiments is set to 4, the second group of simulation experiments is set to 3, and the relaxation parameters are all set to 2; the image reconstruction method in the present invention corrects the inverse proportional parameter in the residual function of the first group A=40 , the second group A=20.

It can be seen from Figure 2 and Figure 3 that there are a lot of noise in the low-resolution images in the two sets of simulation experiments, and at the same time, due to the violent movement, the motion prediction of the image frame will cause great errors, and the first method cannot effectively solve the above problems , the result obtained after this processing has a part of detail loss, especially on the table line, and at the same time, the image is very noisy (as shown in (c) in Figure 2 and (c) in Figure 3).

However, the super-resolution image reconstruction method based on the space-time transformation technology in the present invention can not only effectively reduce noise amplification, but also reduce prediction errors caused by strong motion. From the part (d) in Figure 2 and the part (d) in Figure 3, it can be seen that the image details are clearer, the edge part of the image is significantly improved compared with the processing result of method 1, and the noise is also well controlled, so that the image Excellent quality.

The following table 1 shows the actual indicators corresponding to method one and the image reconstruction method in the present invention in the iterative process when two groups of simulation experiments are carried out, and accompanying drawings 4 and 5 respectively show method one and the image reconstruction method in the present invention in the iterative process The change curve occurs when the number of iterations of the actual index corresponding to the process changes.

Table 1 Reconstructed images and real-world indicators of different methods

According to the comparison of the curves, it is found that the number of iterations is constantly increasing, even though the signal-to-noise ratio and the mean square error results of the two methods are very close to stable, but the value of the signal-to-noise ratio of the method of the present invention is larger, and the value of the mean square error is smaller , improve the signal-to-noise ratio of the reconstructed image and reduce the mean square error, so that the reconstructed image has an excellent vision. This proves that the super-resolution image reconstruction method proposed in this paper has high effectiveness.

The basic principles, main features and advantages of the present invention have been shown and described above. Those skilled in the industry should understand that the present invention is not limited by the above-mentioned embodiments. What are described in the above-mentioned embodiments and the description only illustrate the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will also have Variations and improvements are possible, which fall within the scope of the claimed invention. The protection scope of the present invention is defined by the appended claims and their equivalents.

Claims (5)

1. The super-resolution image reconstruction method based on space-time transformation technology, is characterized in that, comprises the following steps, S1: Divide the image into three components of R, G and B by means of components; S2: Compose the R, G and B components of each low-resolution image sequence into vectors l _R , l _G , l _B , where l _R , l _G , and l _B represent the vectors of all low-resolution observation values in the corresponding components ; S3: Use the space-time transformation technology to construct the contribution matrices A _R , A _G , A _B of each high-resolution space-time point corresponding to the low-resolution space-time point; S4: Use the linear formula Ah=l of high-resolution elements to obtain the vectors h _R , h _G , h _B of the high-time resolution image sequence; where, h _R , h _G , h _B represent all the reconstructed image frame sequences X different component vectors of unknown high-resolution values; S5: Reconstruct the spatial super-resolution according to the h _R , h _G and h _B values obtained in step S4, and obtain X _R , X _G and X _B corresponding to the R, G and B components in the super-resolution image sequence; S6: Combining R, G and B components X _R , X _G and X _B to finally obtain a super-resolution image; The concrete operation of step S3 comprises the following steps, S31: Perform matching processing on the low-resolution image sequences to obtain N low-resolution image sequences, perform temporal and spatial downsampling on the observation models of the N low-resolution image sequences, and obtain N sampling matrices D ₁ and D ₂ based on temporal and spatial transformations, ..., D _N ; S32: Find out that the object space will not change the coordinates of each point in the space with the movement of the field of view, and obtain the space-time coordinate transformation matrices T ₁ , T ₂ , ..., T _N of N low-resolution images; S33: Obtain camera point spread functions H ₁ , H ₂ , ..., H _N of N low-resolution images, and time blur matrices M ₁ , M ₂ , ..., M _N corresponding to the low-resolution image sequences; S34: Establish observation models of several images; S35: From the observation model, it can be concluded that the relationship between the i-th low-resolution image sequence and the predicted high-resolution sequence X is Y _i =D _i M _i H _i T _i X+n _i , 1≤i≤N , where N _i represents the observation noise of the i-th low-resolution image; Y _i is also the contribution matrix A of the low-resolution spatio-temporal points corresponding to each high-resolution spatio-temporal point; S36: The R, G and B components of the contribution matrix A of the low-resolution space-time point corresponding to each high-resolution space-time point are the contribution matrices A _R , A _G , A _B . 2. The super-resolution image reconstruction method based on spatio-temporal transformation technology according to claim 1, characterized in that in step S4, the vectors h _R , h _G , h _B of the high temporal resolution image sequence are obtained by using the conjugate gradient algorithm. 3. The super-resolution image reconstruction method based on spatio-temporal transformation technology according to claim 2, characterized in that, the specific operations of obtaining the vectors h _R , h _G , h _B of the high temporal resolution image sequence using the conjugate gradient algorithm include Following steps, S41: According to the linear formula Ah=l of high-resolution elements, the least square image sequence model minE(h)=min{||Ah-l|| ² } can be obtained; S42: Normalize the least square image sequence model to obtain the image sequence super-resolution reconstruction equation minE(h)=min{||Ah-l|| ² +α||WCh|| ² }; where, W represents the diagonal weight matrix function that records the expected normalization at each time point; α represents the overall normalization factor; C represents the matrix that records the space-time square valence derivative, which is selected as the laplace operator; S43: Initially set β=0, h ₀ =0, b= ^AT l, r=b, p=b; S44: Carry out iterative operation from k=1, 2..., wherein, the algorithm search direction is p=r+βp, q=(A ^T A+αC ^T W ^T WC)p; the algorithm search step size is α=r ^T r/p ^T p, the algorithm gradient is r ₀ = r, r = r ₀ -αq,

S45: Then obtain the actual search h _k =h _k-1 +αp, where h=h _R , h _G , h _B . 4. The super-resolution image reconstruction method based on spatio-temporal transformation technology according to claim 3, characterized in that step S5 uses an iterative back-projection method to perform spatial super-resolution reconstruction. 5. the super-resolution image reconstruction method based on spatio-temporal transformation technology according to claim 4, is characterized in that, the method that uses iterative back projection mode to carry out spatial super-resolution reconstruction can be expressed as

Among them, m is described as the number of iterations; p is described as the number of frames in the low-resolution image; />

Described as the super-resolution image frame obtained by the m+1th iteration; />

Described as the super-resolution image frame obtained by the mth iteration; />

Described as the number of iterative backprojection practices; />

described as />

A low-resolution image frame experimentally obtained in a low-resolution observation model; λ is described as the gradient step size; f is described as the reference frame; Δ is described as the Laplace operator of the quadratic valence differential.

Images